A new tower with good $p$-rank meeting Zink’s bound
Volume 177 / 2017
Acta Arithmetica 177 (2017), 347-374
MSC: Primary 14H05, 11G20; Secondary 14G50.
DOI: 10.4064/aa8388-6-2016
Published online: 18 January 2017
Abstract
We investigate the asymptotic $p$-rank of a new tower of function fields defined over cubic finite fields. Its limit meets Zink’s bound, but the new feature of this tower is that its asymptotic $p$-rank for small cubic finite fields is much smaller than that of other cubic towers for which the asymptotic $p$-rank is known. This is of independent interest, but also makes this new tower more interesting for theoretical applications in cryptography.
